{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overfitting vs. Underfitting\n",
    "\n",
    "Exploring a fundamental problem in modeling. This notebook will look at a simple example showing the problem of overfitting and underfitting as well as how to address it via cross-validation. This example is based on the [scikit-learn exercise](http://scikit-learn.org/stable/auto_examples/model_selection/plot_underfitting_overfitting.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports \n",
    "\n",
    "We will use numpy and pandas, two of the most common libraries for data manipulation. We use scikit-learn, a popular machine learning library, for creating and evaluating the models. Matplotlib is used for model visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Numpy and pandas as usual\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# Scikit-Learn for fitting models\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "# For plotting in the notebook\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# Default parameters for plots\n",
    "matplotlib.rcParams['font.size'] = 12\n",
    "matplotlib.rcParams['figure.titlesize'] = 16\n",
    "matplotlib.rcParams['figure.figsize'] = [9, 7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate a relationship\n",
    "\n",
    "First, we need a \"true\" relationship. We define a curve, in this case a sine curve to serve as our process that generates the data. As the real-world is never perfectly celan however, we also need to add some noise into the observations. This is done by adding a small random number to each value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the random seed for reproducible results\n",
    "np.random.seed(42)\n",
    "\n",
    "# \"True\" generating function representing a process in real life\n",
    "def true_gen(x):\n",
    "    y = np.sin(1.2 * x * np.pi) \n",
    "    return(y)\n",
    "\n",
    "# x values and y value with a small amount of random noise\n",
    "x = np.sort(np.random.rand(120))\n",
    "y = true_gen(x) + 0.1 * np.random.randn(len(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training and Testing Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Random indices for creating training and testing sets\n",
    "random_ind = np.random.choice(list(range(120)), size = 120, replace=False)\n",
    "xt = x[random_ind]\n",
    "yt = y[random_ind]\n",
    "\n",
    "# Training and testing observations\n",
    "train = xt[:int(0.7 * len(x))]\n",
    "test = xt[int(0.7 * len(x)):]\n",
    "\n",
    "y_train = yt[:int(0.7 * len(y))]\n",
    "y_test = yt[int(0.7 * len(y)):]\n",
    "\n",
    "# Model the true curve\n",
    "x_linspace = np.linspace(0, 1, 1000)\n",
    "y_true = true_gen(x_linspace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d1b2828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize observations and true curve\n",
    "plt.plot(train, y_train, 'ko', label = 'Train'); \n",
    "plt.plot(test, y_test, 'ro', label = 'Test')\n",
    "plt.plot(x_linspace, y_true, 'b-', linewidth = 2, label = 'True Function')\n",
    "plt.legend()\n",
    "plt.xlabel('x'); plt.ylabel('y'); plt.title('Data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Model\n",
    "\n",
    "We want to try and capture the data using a polynomial function. A polynomial is defined by the degree, or the highest power to for the x-values. A line has a degree of 1 because it is of the form $y = b_1*x + b_0$ where $b_1$ is the slope and $b_0$ is the intercept. A third degree polynomial would have the form $y = b_3 * x^3 + b_2 * x^2 + b_1 * x + b_0$ and so on. The higher the degree of the polynomial, the more flexible the model. A more flexible model is prone to overfitting because it can can \"bend\" to follow the training data.  \n",
    "\n",
    "The following function creates a polynomial with the specified number of degrees and plots the results. We can use these results to determine the optimal degrees to achieve the right balance between over and underfitting. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def fit_poly(train, y_train, test, y_test, degrees, plot='train', return_scores=False):\n",
    "    \n",
    "    # Create a polynomial transformation of features\n",
    "    features = PolynomialFeatures(degree=degrees, include_bias=False)\n",
    "    \n",
    "    # Reshape training features for use in scikit-learn and transform features\n",
    "    train = train.reshape((-1, 1))\n",
    "    train_trans = features.fit_transform(train)\n",
    "    \n",
    "    # Create the linear regression model and train\n",
    "    model = LinearRegression()\n",
    "    model.fit(train_trans, y_train)\n",
    "    \n",
    "    # Calculate the cross validation score\n",
    "    cross_valid = cross_val_score(model, train_trans, y_train, scoring='neg_mean_squared_error', cv = 5)\n",
    "    \n",
    "    # Training predictions and error\n",
    "    train_predictions = model.predict(train_trans)\n",
    "    training_error = mean_squared_error(y_train, train_predictions)\n",
    "    \n",
    "    # Format test features\n",
    "    test = test.reshape((-1, 1))\n",
    "    test_trans = features.fit_transform(test)\n",
    "    \n",
    "    # Test set predictions and error\n",
    "    test_predictions = model.predict(test_trans)\n",
    "    testing_error = mean_squared_error(y_test, test_predictions)\n",
    "    \n",
    "    # Find the model curve and the true curve\n",
    "    x_curve = np.linspace(0, 1, 100)\n",
    "    x_curve = x_curve.reshape((-1, 1))\n",
    "    x_curve_trans = features.fit_transform(x_curve)\n",
    "    \n",
    "    # Model curve\n",
    "    model_curve = model.predict(x_curve_trans)\n",
    "    \n",
    "    # True curve\n",
    "    y_true_curve = true_gen(x_curve[:, 0])\n",
    "    \n",
    "    # Plot observations, true function, and model predicted function\n",
    "    if plot == 'train':\n",
    "        plt.plot(train[:, 0], y_train, 'ko', label = 'Observations')\n",
    "        plt.plot(x_curve[:, 0], y_true_curve, linewidth = 4, label = 'True Function')\n",
    "        plt.plot(x_curve[:, 0], model_curve, linewidth = 4, label = 'Model Function')\n",
    "        plt.xlabel('x'); plt.ylabel('y')\n",
    "        plt.legend()\n",
    "        plt.ylim(-1, 1.5); plt.xlim(0, 1)\n",
    "        plt.title('{} Degree Model on Training Data'.format(degrees))\n",
    "        plt.show()\n",
    "        \n",
    "    elif plot == 'test':\n",
    "        # Plot the test observations and test predictions\n",
    "        plt.plot(test, y_test, 'o', label = 'Test Observations')\n",
    "        plt.plot(x_curve[:, 0], y_true_curve, 'b-', linewidth = 2, label = 'True Function')\n",
    "        plt.plot(test, test_predictions, 'ro', label = 'Test Predictions')\n",
    "        plt.ylim(-1, 1.5); plt.xlim(0, 1)\n",
    "        plt.legend(), plt.xlabel('x'), plt.ylabel('y'); plt.title('{} Degree Model on Testing Data'.format(degrees)), plt.show();\n",
    "    \n",
    "    # Return the metrics\n",
    "    if return_scores:\n",
    "        return training_error, testing_error, -np.mean(cross_valid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try Model with Different Degrees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Degrees = 1 -> Underfitting\n",
    "\n",
    "In this case, a linear model cannot accurate learn the relationship between x and y and will underfit the data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d1d5390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, degrees = 1, plot='train')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d1d51d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, degrees = 1, plot='test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Degrees = 25 -> Overfitting\n",
    "\n",
    "We can go in the completely opposite direction and create a model that overfits the data. This model has too much flexibility and learns the training data too closely. As the training data has some amount of noise, it will end up capturing that noise and will be misled by that noise when it tries to make predictions on the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5465f5588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, plot='train', degrees = 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54b8b56d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, degrees=25, plot='test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Degrees = 5 -> Balanced Model\n",
    "\n",
    "Now that we have seen the two extremes, we can take a look at a model that does a good job of both accounting for the data while not following it too closely. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d108b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, plot='train', degrees = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d1bc518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, degrees=5, plot='test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross Validation\n",
    "\n",
    "To pick the optimal model, we need to use a validation set. Cross validation is even better than a single validation set because it uses numerous validation sets created from the training data. In this case, we are using 5 different validation sets. The model that performs best on the cross validation is usually the optimal model because it has shown that it can learn the relationships while not overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Range of model degrees to evaluate\n",
    "degrees = [int(x) for x in np.linspace(1, 40, 40)]\n",
    "\n",
    "# Results dataframe\n",
    "results = pd.DataFrame(0, columns = ['train_error', 'test_error', 'cross_valid'], index = degrees)\n",
    "\n",
    "# Try each value of degrees for the model and record results\n",
    "for degree in degrees:\n",
    "    degree_results = fit_poly(train, y_train, test, y_test, degree, plot=False, return_scores=True)\n",
    "    results.ix[degree, 'train_error'] = degree_results[0]\n",
    "    results.ix[degree, 'test_error'] = degree_results[1]\n",
    "    results.ix[degree, 'cross_valid'] = degree_results[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 Lowest Cross Validation Errors\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>degrees</th>\n",
       "      <th>cross_valid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>0.010549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>0.010637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>0.010665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>0.010887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>0.011182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>0.011695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9</td>\n",
       "      <td>0.011757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>11</td>\n",
       "      <td>0.011769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>10</td>\n",
       "      <td>0.011902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>12</td>\n",
       "      <td>0.012642</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   degrees  cross_valid\n",
       "0        4     0.010549\n",
       "1        5     0.010637\n",
       "2        7     0.010665\n",
       "3        6     0.010887\n",
       "4        8     0.011182\n",
       "5        3     0.011695\n",
       "6        9     0.011757\n",
       "7       11     0.011769\n",
       "8       10     0.011902\n",
       "9       12     0.012642"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('10 Lowest Cross Validation Errors\\n')\n",
    "train_eval = results.sort_values('cross_valid').reset_index(level=0).rename(columns={'index': 'degrees'})\n",
    "train_eval.ix[:,['degrees', 'cross_valid']] .head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum Cross Validation Error occurs at 4 degrees.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d4c7240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(results.index, results['cross_valid'], 'go-', ms=6)\n",
    "plt.xlabel('Degrees'); plt.ylabel('Cross Validation Error'); plt.title('Cross Validation Results');\n",
    "plt.ylim(0, 0.2);\n",
    "print('Minimum Cross Validation Error occurs at {} degrees.\\n'.format(int(np.argmin(results['cross_valid']))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final Model\n",
    "\n",
    "The model with the lowest cross validation error had four degrees. Therefore, we will use a 4th degree polynomial for the final model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d1e72e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, degrees=4, plot='train')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d1d54e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_poly(train, y_train, test, y_test, degrees=4, plot='test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate Models \n",
    "\n",
    "The next step is to examine the scores for the models. We will use a range of values to see how the performance on the training and testing set compares. A model with much lower errors on the training data than the testing data is overfit. A model with high error on the training data (which will lead to high testing error as well) is underfitting because it does not even learn the training data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Quantitative Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 Lowest Training Errors\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>degrees</th>\n",
       "      <th>train_error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>35</td>\n",
       "      <td>0.006121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>36</td>\n",
       "      <td>0.006142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>40</td>\n",
       "      <td>0.006192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>39</td>\n",
       "      <td>0.006272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31</td>\n",
       "      <td>0.006367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>27</td>\n",
       "      <td>0.006405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>32</td>\n",
       "      <td>0.006412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>28</td>\n",
       "      <td>0.006432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>33</td>\n",
       "      <td>0.006441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>29</td>\n",
       "      <td>0.006467</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   degrees  train_error\n",
       "0       35     0.006121\n",
       "1       36     0.006142\n",
       "2       40     0.006192\n",
       "3       39     0.006272\n",
       "4       31     0.006367\n",
       "5       27     0.006405\n",
       "6       32     0.006412\n",
       "7       28     0.006432\n",
       "8       33     0.006441\n",
       "9       29     0.006467"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('10 Lowest Training Errors\\n')\n",
    "train_eval = results.sort_values('train_error').reset_index(level=0).rename(columns={'index': 'degrees'})\n",
    "train_eval.ix[:,['degrees', 'train_error']] .head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 Lowest Testing Errors\n",
      "\n"
     ]
    },
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>degrees</th>\n",
       "      <th>test_error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>0.009482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>0.010215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>0.010483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>0.010609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7</td>\n",
       "      <td>0.010618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>10</td>\n",
       "      <td>0.011321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>11</td>\n",
       "      <td>0.011342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>13</td>\n",
       "      <td>0.011387</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   degrees  test_error\n",
       "0        5    0.009482\n",
       "1        6    0.010215\n",
       "2        4    0.010483\n",
       "3        8    0.010609\n",
       "4        7    0.010618\n",
       "5        9    0.010754\n",
       "6       14    0.011216\n",
       "7       10    0.011321\n",
       "8       11    0.011342\n",
       "9       13    0.011387"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('10 Lowest Testing Errors\\n')\n",
    "train_eval = results.sort_values('test_error').reset_index(level=0).rename(columns={'index': 'degrees'})\n",
    "train_eval.ix[:,['degrees', 'test_error']] .head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visual Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e54d422518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Minimum Training Error occurs at 35 degrees.\n",
      "Minimum Testing Error occurs at 5 degrees.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plt.plot(results.index, results['train_error'], 'b-o', ms=6, label = 'Training Error')\n",
    "plt.plot(results.index, results['test_error'], 'r-*', ms=6, label = 'Testing Error')\n",
    "plt.legend(loc=2); plt.xlabel('Degrees'); plt.ylabel('Mean Squared Error'); plt.title('Training and Testing Curves');\n",
    "plt.ylim(0, 0.05); plt.show()\n",
    "\n",
    "print('\\nMinimum Training Error occurs at {} degrees.'.format(int(np.argmin(results['train_error']))))\n",
    "print('Minimum Testing Error occurs at {} degrees.\\n'.format(int(np.argmin(results['test_error']))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
